The influence of the place-value structure of the Arabic number ...

positively correlated with overall performance in the third grade addition task. This indicated
that children who committed relatively more errors in either transcoding or number
comparison also exhibited a higher error rate in an addition task administered two years later
(see Table 2, Panel A). Furthermore, in the current data set no reliable association between
addition performance and either intelligence or WM capacity could be observed (see Table 2,
Panel A). So, only the numerical predictors in first grade were associated reliably with
addition performance in third grade, while the non-numerical variables did not predict any
variance in the addition task.
When running a multiple stepwise regression analysis incorporation all variables of
the correlation matrix in Table 1, Panel A to evaluate the differential influences of overall
comparison and/or transcoding performance on overall addition performance, overall
performance in the magnitude comparison task turned out to be the only reliable predictor [b
= .25, t = 2.48, p < .05] incorporated in the model [R = .25, adjusted R 2 = .05, F(2, 92) = 6.13,
p < .05, f 2 = .07]. As already indicated by the positive correlation, a higher error rate in the
magnitude comparison task in grade one was associated with a higher error rate in the
addition task two years later. The fact that overall transcoding performance was not found to
be a reliable predictor of overall addition performance may be attributed to the very high
intercorrelation of overall performance in magnitude comparison and transcoding (see Table
2, Panel A).
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